HAAPASALO, Erkka, Michal SEDLÁK and Mário ZIMAN. Distance to boundary and minimum-error discrimination. Physical Review A. 2014, vol. 89, No 6, p. 1-12. ISSN 1050-2947. Available from: https://dx.doi.org/10.1103/PhysRevA.89.062303.
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Basic information
Original name Distance to boundary and minimum-error discrimination
Authors HAAPASALO, Erkka (246 Finland), Michal SEDLÁK (203 Czech Republic) and Mário ZIMAN (703 Slovakia, guarantor, belonging to the institution).
Edition Physical Review A, 2014, 1050-2947.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10301 Atomic, molecular and chemical physics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 2.808
RIV identification code RIV/00216224:14330/14:00073909
Organization unit Faculty of Informatics
Doi http://dx.doi.org/10.1103/PhysRevA.89.062303
UT WoS 000336906100006
Keywords in English quantum information theory - quantum discrimination - convex analysis
Changed by Changed by: RNDr. Pavel Šmerk, Ph.D., učo 3880. Changed: 27/4/2015 04:22.
Abstract
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any explicit topology) how far the given element is from the boundary. It is shown that one of the elements from the boundary can be always chosen to be an extremal element. We focus on evaluation of this quantity for quantum sets of states, channels, and observables. We show that boundariness is intimately related to (semi)norms that provide an operational interpretation of this quantity. In particular, the minimum error probability for discrimination of a pair of quantum devices is lower bounded by the boundariness of each of them. We proved that for states and observables this bound is saturated and conjectured this feature for channels. The boundariness is zero for infinite-dimensional quantum objects as in this case all the elements are boundary elements.
Links
GAP202/12/1142, research and development projectName: Slabé zdroje entanglementu a náhodnosti
Investor: Czech Science Foundation
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